Warm-up: Simplify: Solve: 1) (3x + 2y) – 2(x + y) 2) y2 + (y – 2)2 = 2 HW: pages 581-582 (1-10, 11-14) and 593-594 (1-20)

Higher order equations are often best solved with this method. Try Substitute both answers into the easiest equation. Check both equations.

Elimination-this is also called linear combination or addition-subtraction method. It is a good method when the equations come in standard form. It requires that you find a multiple or multiples that will enable you to eliminate one of the variables by creating opposites. We will use 4 on the first equation and 3 on the second to eliminate y, solve for x. 4(5x + 3y = 9) 20x + 12y = 36 3(2x – 4y = 14) 6x – 12y = 42 26x = 78 x = 3 Next is to substitute in x = 3 to find y. Finally, check using both equations.

Example: 2x - 3y = -7 3x + y = -5

Try graphing and don’t forget to check. Graphing-the graphing method is great IF you have access to a graphing calculator and know how to use it. It is also an important method to see solutions as intersections. Try graphing and don’t forget to check. (1, 0) ?

Graphing is also good for noticing when there is no solution as in these next two problems. See what happens when you solve these two algebraically.

There is also what we call coinciding where there are infinite solutions. If you were to try and graph them you would notice right away that they are the same.

Reading the solution as (3, -2) Special Method-Finally we have a method that is totally dependent on the calculator. It is called row reduced echelon function. You will need to be able to enter the equation into the matrix function of the calculator. They need to be in standard form, Ax+By=C. Then you will use the matrix math function, rref on your matrix. We will try and Editting the matrix. Using matrix math. Reading the solution as (3, -2)

Now try x + y = 4 and x – y = 2 . You should get (3, 1). Advice; 1. Fractions and decimals should be multiplied out first. 2. Always check using ALL equations!!! HW: pages 581-582 (1-10, 11-14) and 593-594 (1-20)